Curriculum  /  Math  /  11th Grade  /  Unit 4: Rational and Radical Functions  /  Lesson 7

Rational and Radical Functions

Lesson 7

Math

Unit 4

11th Grade

Lesson 7 of 18

Objective

Add and subtract rational expressions.

Common Core Standards

Core Standards

  • A.APR.D.6 — Rewrite simple rational expressions in different forms; write a(x /b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
  • A.APR.D.7 — Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Foundational Standards

  • A.APR.A.1

Criteria for Success

  1. Identify the common denominators of an algebraic expression. 
  2. Describe how adding numerical fractions with unlike denominators requires the same process as adding or subtracting rational expressions with variables. 
  3. Calculate equivalent rational terms through use of common denominators.
  4. Factor or manipulate expressions in ways such that you will be able to find the least common multiple of two denominators. 
  5. Identify domain restrictions on rational expressions. 
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Anchor Problems

25-30 minutes

Problem 1

Find the sum of the following two terms: 

$${{3\over{n}}+{8\over{n+1}}}$$

Guiding Questions

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Problem 2

Subtract the following two terms: 

$${{4\over{n-1}}-{5+n\over4}}$$

Guiding Questions

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Problem 3

Find the sum of the following two terms: 
$${{8+x\over{x^2-6x+8}}+{3-2x\over{x^2-3x-4}}}$$

Guiding Questions

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Target Task

5-10 minutes

Problem 1

Subtract the following two terms. 
$${{4r\over{r+3}}-{5\over{r}}}$$

References

EngageNY Mathematics Algebra II > Module 1 > Topic C > Lesson 25 — Exit Ticket

Algebra II > Module 1 > Topic C > Lesson 25 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

Add the following two terms. 

$${{x-2\over{x+4}}+{3-2x\over3}}$$

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems about domain restrictions as well as radicals and rational exponents to provide consistent review throughout the unit. 

Next

Identify asymptotic discontinuities (also known as infinite discontinuities) and removable discontinuities in a rational function and describe why these discontinuities exist.

Lesson 8
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Introduction to Rational and Radical Functions and Expressions

Topic B: Features of Rational Functions and Graphing Rational Functions

Topic C: Solve Rational and Radical Equations and Model with Rational Functions

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